Type Alias Scale4

pub type Scale4<T> = Scale<T, 4>;

A 4-dimensional scale.

Aliased Type

struct Scale4<T> {
    pub vector: Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>,
}

Fields

vector: Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>

The scale coordinates, i.e., how much is multiplied to a point’s coordinates when it is scaled.

Implementations

impl<T> Scale<T, 4>

pub const fn new(x: T, y: T, z: T, w: T) -> Self

Initializes this Scale from its components.

Example

let t = Scale4::new(1.0, 2.0, 3.0, 4.0);
assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0);

impl<T: Scalar, const D: usize> Scale<T, D>

pub fn try_inverse(&self) -> Option<Scale<T, D>>

where T: ClosedDiv + One + Zero,

Inverts self.

Example

let t = Scale3::new(1.0, 2.0, 3.0);
assert_eq!(t * t.try_inverse().unwrap(), Scale3::identity());
assert_eq!(t.try_inverse().unwrap() * t, Scale3::identity());

// Work in all dimensions.
let t = Scale2::new(1.0, 2.0);
assert_eq!(t * t.try_inverse().unwrap(), Scale2::identity());
assert_eq!(t.try_inverse().unwrap() * t, Scale2::identity());

// Returns None if any coordinate is 0.
let t = Scale2::new(0.0, 2.0);
assert_eq!(t.try_inverse(), None);

pub unsafe fn inverse_unchecked(&self) -> Scale<T, D>

where T: ClosedDiv + One,

Inverts self.

Example

unsafe {
    let t = Scale3::new(1.0, 2.0, 3.0);
    assert_eq!(t * t.inverse_unchecked(), Scale3::identity());
    assert_eq!(t.inverse_unchecked() * t, Scale3::identity());

    // Work in all dimensions.
    let t = Scale2::new(1.0, 2.0);
    assert_eq!(t * t.inverse_unchecked(), Scale2::identity());
    assert_eq!(t.inverse_unchecked() * t, Scale2::identity());
}

pub fn pseudo_inverse(&self) -> Scale<T, D>

where T: ClosedDiv + One + Zero,

Inverts self.

Example

let t = Scale3::new(1.0, 2.0, 3.0);
assert_eq!(t * t.pseudo_inverse(), Scale3::identity());
assert_eq!(t.pseudo_inverse() * t, Scale3::identity());

// Work in all dimensions.
let t = Scale2::new(1.0, 2.0);
assert_eq!(t * t.pseudo_inverse(), Scale2::identity());
assert_eq!(t.pseudo_inverse() * t, Scale2::identity());

// Inverts only non-zero coordinates.
let t = Scale2::new(0.0, 2.0);
assert_eq!(t * t.pseudo_inverse(), Scale2::new(0.0, 1.0));
assert_eq!(t.pseudo_inverse() * t, Scale2::new(0.0, 1.0));

pub fn to_homogeneous( &self, ) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

where T: Zero + One + Clone, Const<D>: DimNameAdd<U1>, DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T, DimNameSum<Const<D>, U1>, U1>,

Converts this Scale into its equivalent homogeneous transformation matrix.

Example

let t = Scale3::new(10.0, 20.0, 30.0);
let expected = Matrix4::new(10.0, 0.0, 0.0, 0.0,
                            0.0, 20.0, 0.0, 0.0,
                            0.0, 0.0, 30.0, 0.0,
                            0.0, 0.0, 0.0, 1.0);
assert_eq!(t.to_homogeneous(), expected);

let t = Scale2::new(10.0, 20.0);
let expected = Matrix3::new(10.0, 0.0, 0.0,
                            0.0, 20.0, 0.0,
                            0.0, 0.0, 1.0);
assert_eq!(t.to_homogeneous(), expected);

pub fn try_inverse_mut(&mut self) -> bool

where T: ClosedDiv + One + Zero,

Inverts self in-place.

Example

let t = Scale3::new(1.0, 2.0, 3.0);
let mut inv_t = Scale3::new(1.0, 2.0, 3.0);
assert!(inv_t.try_inverse_mut());
assert_eq!(t * inv_t, Scale3::identity());
assert_eq!(inv_t * t, Scale3::identity());

// Work in all dimensions.
let t = Scale2::new(1.0, 2.0);
let mut inv_t = Scale2::new(1.0, 2.0);
assert!(inv_t.try_inverse_mut());
assert_eq!(t * inv_t, Scale2::identity());
assert_eq!(inv_t * t, Scale2::identity());

// Does not perform any operation if a coordinate is 0.
let mut t = Scale2::new(0.0, 2.0);
assert!(!t.try_inverse_mut());

impl<T: Scalar + ClosedMul, const D: usize> Scale<T, D>

pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, D>

Translate the given point.

This is the same as the multiplication self * pt.

Example

let t = Scale3::new(1.0, 2.0, 3.0);
let transformed_point = t.transform_point(&Point3::new(4.0, 5.0, 6.0));
assert_eq!(transformed_point, Point3::new(4.0, 10.0, 18.0));

impl<T: Scalar + ClosedDiv + ClosedMul + One + Zero, const D: usize> Scale<T, D>

pub fn try_inverse_transform_point( &self, pt: &Point<T, D>, ) -> Option<Point<T, D>>

Translate the given point by the inverse of this Scale.

Example

let t = Scale3::new(1.0, 2.0, 3.0);
let transformed_point = t.try_inverse_transform_point(&Point3::new(4.0, 6.0, 6.0)).unwrap();
assert_eq!(transformed_point, Point3::new(4.0, 3.0, 2.0));

// Returns None if the inverse doesn't exist.
let t = Scale3::new(1.0, 0.0, 3.0);
let transformed_point = t.try_inverse_transform_point(&Point3::new(4.0, 6.0, 6.0));
assert_eq!(transformed_point, None);

impl<T: Scalar, const D: usize> Scale<T, D>

pub fn identity() -> Scale<T, D>

where T: One,

Creates a new identity scale.

Example

let t = Scale2::identity();
let p = Point2::new(1.0, 2.0);
assert_eq!(t * p, p);

// Works in all dimensions.
let t = Scale3::identity();
let p = Point3::new(1.0, 2.0, 3.0);
assert_eq!(t * p, p);

pub fn cast<To: Scalar>(self) -> Scale<To, D>

where Scale<To, D>: SupersetOf<Self>,

Cast the components of self to another type.

Example

let tra = Scale2::new(1.0f64, 2.0);
let tra2 = tra.cast::<f32>();
assert_eq!(tra2, Scale2::new(1.0f32, 2.0));

Trait Implementations

impl<T: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Scale<T, D>

where T::Epsilon: Clone,

type Epsilon = <T as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<T: Clone, const D: usize> Clone for Scale<T, D>

fn clone(&self) -> Scale<T, D>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug, const D: usize> Debug for Scale<T, D>

fn fmt(&self, formatter: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T: Scalar> Deref for Scale<T, 4>

type Target = XYZW<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar> DerefMut for Scale<T, 4>

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<'a, T: Scalar, const D: usize> Deserialize<'a> for Scale<T, D>

where Owned<T, Const<D>>: Deserialize<'a>,

fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>

where Des: Deserializer<'a>,

Deserialize this value from the given Serde deserializer.

impl<T: Scalar + Display, const D: usize> Display for Scale<T, D>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 16]> for Scale<T, D>

where T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue, T::Element: Scalar,

fn from(arr: [Scale<T::Element, D>; 16]) -> Self

Converts to this type from the input type.

impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 2]> for Scale<T, D>

where T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue, T::Element: Scalar,

fn from(arr: [Scale<T::Element, D>; 2]) -> Self

Converts to this type from the input type.

impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 4]> for Scale<T, D>

where T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue, T::Element: Scalar,

fn from(arr: [Scale<T::Element, D>; 4]) -> Self

Converts to this type from the input type.

impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 8]> for Scale<T, D>

where T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue, T::Element: Scalar,

fn from(arr: [Scale<T::Element, D>; 8]) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<[T; D]> for Scale<T, D>

fn from(coords: [T; D]) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Matrix<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<T, Const<D>>>::Buffer>> for Scale<T, D>

fn from(vector: OVector<T, Const<D>>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<OPoint<T, Const<D>>> for Scale<T, D>

fn from(pt: Point<T, D>) -> Self

Converts to this type from the input type.

impl<T: Scalar + Hash, const D: usize> Hash for Scale<T, D>

where Owned<T, Const<D>>: Hash,

fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<'b, T, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = OPoint<T, Const<D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b Scale<T, D>> for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Scale<T, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Scale<T, D>) -> Self::Output

Performs the * operation.

impl<T, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<T, const D: usize> Mul<OPoint<T, Const<D>>> for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = OPoint<T, Const<D>>

The resulting type after applying the * operator.

fn mul(self, right: Point<T, D>) -> Self::Output

Performs the * operation.

impl<T, const D: usize> Mul<T> for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Scale<T, D>

The resulting type after applying the * operator.

fn mul(self, right: T) -> Self::Output

Performs the * operation.

impl<T, const D: usize> Mul for Scale<T, D>

where T: Scalar + ClosedMul, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Scale<T, D>

The resulting type after applying the * operator.

fn mul(self, right: Scale<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, const D: usize> MulAssign<&'b Scale<T, D>> for Scale<T, D>

where T: Scalar + ClosedMul,

fn mul_assign(&mut self, right: &'b Scale<T, D>)

Performs the *= operation.

impl<T, const D: usize> MulAssign<T> for Scale<T, D>

where T: Scalar + ClosedMul,

fn mul_assign(&mut self, right: T)

Performs the *= operation.

impl<T, const D: usize> MulAssign for Scale<T, D>

where T: Scalar + ClosedMul,

fn mul_assign(&mut self, right: Scale<T, D>)

Performs the *= operation.

impl<T: Scalar + One + ClosedMul, const D: usize> One for Scale<T, D>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<T: Scalar + PartialEq, const D: usize> PartialEq for Scale<T, D>

fn eq(&self, right: &Scale<T, D>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: Scalar + RelativeEq, const D: usize> RelativeEq for Scale<T, D>

where T::Epsilon: Clone,

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl<T: Scalar, const D: usize> Serialize for Scale<T, D>

where Owned<T, Const<D>>: Serialize,

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<T: Scalar + SimdValue, const D: usize> SimdValue for Scale<T, D>

where T::Element: Scalar,

type Element = Scale<<T as SimdValue>::Element, D>

The type of the elements of each lane of this SIMD value.

type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.

fn lanes() -> usize

The number of lanes of this SIMD value.

fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.

fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking.

fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking.

fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond.

fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self

where Self: Clone,

Applies a function to each lane of self.

fn zip_map_lanes( self, b: Self, f: impl Fn(Self::Element, Self::Element) -> Self::Element, ) -> Self

where Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b.

impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Scale<T1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, Const<D>: DimNameAdd<U1>, DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T1, DimNameSum<Const<D>, U1>, U1> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, const D: usize> SubsetOf<Scale<T2, D>> for Scale<T1, D>

where T1: Scalar, T2: Scalar + SupersetOf<T1>,

fn to_superset(&self) -> Scale<T2, D>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(rot: &Scale<T2, D>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(rot: &Scale<T2, D>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Scale<T1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, C: SuperTCategoryOf<TAffine>, Const<D>: DimNameAdd<U1>, DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T1, DimNameSum<Const<D>, U1>, U1> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset(&self) -> Transform<T2, C, D>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(t: &Transform<T2, C, D>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(t: &Transform<T2, C, D>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T: Scalar + UlpsEq, const D: usize> UlpsEq for Scale<T, D>

where T::Epsilon: Clone,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

impl<T: Copy, const D: usize> Copy for Scale<T, D>

impl<T: Scalar + Eq, const D: usize> Eq for Scale<T, D>